Obama: This was an attack on all of us

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But Hillary Clinton has defended her refusal to use the language he prefers

(CNN)As millions of Americans processed the news that a terror attack had left 49 people dead at a gay nightclub in Orlando, Donald Trump reignited a political debate.

"Is President Obama going to finally mention the words radical Islamic terrorism? If he doesn't he should immediately resign in disgrace!" Trump tweeted moments before President Barack Obama addressed the nation from the White House. He doubled down on those comments in a statement later Sunday that also called on Hillary Clinton to toughen her tone on terror.

As expected, Obama did not utter the words "radical" or "Islam," instead referring to the attack as "an act of terror and an act of hate." Indeed, he has resisted using the term "radical Islam" throughout his presidency despite pressure from Republicans.

Hillary Clinton was asked about the terminology on CNN's "New Day" Monday and made clear she would use the words "radical Islam," but she added an important qualifier.

"From my perspective, it matters what we do more than what we say," she said. "And it mattered we got bin Laden, not what name we called him. I have clearly said we -- whether you call it radical jihadism or radical Islamism, I'm happy to say either. I think they mean the same thing."

Though investigators had yet to officially conclude that the Orlando assailant was inspired by radical Islamic ideology, Sunday's tragedy returns questions over the importance of such terminology to the center of American politics.

Here's a look at why "radical Islam" and "radical Islamic terrorism" are such loaded terms and the arguments for and against using them.

Why do Donald Trump and other Republicans say using the term "radical Islamic terrorism" is so important?

Trump and other Republicans have hewed the same line: If you don't name your enemy, you can't defeat it.

Trump explained his outrage at Obama's refusal to use the term at a campaign rally this spring: "Unless you're going to talk about it, you're not going to solve the damn problem folks. You're not going to solve it."

Trump and other Republicans have argued that the Obama administration fails to understand the enemy -- a key component of which, they argue, is the radical Islamic ideology that is fueling terrorist attacks in the Middle East and increasingly in the West.

Terrorists who perpetrated the most recent attacks in Europe and the U.S. -- like the shootings in San Bernardino, California, and Paris -- all subscribed to radical Islamic ideologies. The White House, Republicans say, shouldn't be afraid to call out the source of this violence.

Do experts back up this reasoning?

For Mark Dubowitz, executive director of the Foundation for the Defense of Democracies, identifying the motivations and ideology behind the terrorist threat is essential to combating it.

"It's always critical to understand the nature and gravity of the threat you face and correctly identify the motivating factors," said Dubowitz. "It's equally critical to understand the ideological motivation of the terrorisms we face so, again, we can correctly identify who's likely to attack and ... mobilize against it."

For example, he said, Islamic terrorism can't be defeated without the help of Muslim communities around the world.

He added that while "it's dangerous and foolhardy to besmirch all Muslims," it's "equally foolhardy" not to understand that Islamism "is a political ideology which borrows from Islam and is motivated by Islam," even though it only represents a tiny minority of Muslims.

Other terrorism experts, however, tend to disagree with the take of FDD -- a conservative-leaning think tank that focuses on foreign policy and combatting terrorism -- over the issue of rhetoric, pointing out that the administration has clearly spoken about ISIS as a group inspired by a perverted form of Islam.

So why are Obama and Hillary Clinton so vigorously opposed to this language?

The core of their argument is that associating terrorists with Islam helps to legitimize their interpretation of the religion and does a disservice to the majority of Muslims who don't believe there's anything Islamic about barbaric groups like ISIS, also known as ISIL.

"We are not at war with Islam. We are at war with people who have perverted Islam," Obama said during remarks at a summit on combating violent extremism in February. "These terrorists are desperate for legitimacy. And all of us have a responsibility to refute the notion that groups like ISIL somehow represent Islam, because that is a falsehood that embraces the terrorist narrative."

Clinton, the presumptive Democratic nominee, has defended her refusal to use the term along similar lines.

"That sounds like we are declaring war against a religion," Clinton said in an interview with ABC News in December.

"Number one, it doesn't do justice to the vast numbers of Muslims in our own country and around the world who are peaceful people. Number two, it helps to create this clash of civilizations that is actually a recruiting tool for ISIS and other radical jihadists who use this as a way of saying, 'We're in a war against the West. You must join us. If you are Muslim, you must join us,'" she said in the interview.

Terrorist groups like ISIS have sought to radicalize Muslims living in non-Muslim countries by defining jihad in the context of an "us versus them" mentality, in particular pointing to foreign interventions in Muslim countries as attacks on all Muslims.

Do experts back up this line of thinking?

Most terrorism experts believe that labeling terror attacks as radical Islamic terrorism is either detrimental to efforts to combat them or simply not strategically important to defeating terrorist groups like ISIS and their ideology.

The rhetorical battle has little to do with the nuts-and-bolts fight against these groups, said Daniel Serwer, a scholar at the Middle East Institute and director of the Conflict Management Program at Johns Hopkins University's School of Advanced International Studies.

"ISIS claims a connection to Islam, but are we better off accepting the ISIS claim rather than believing the many Muslims who say terrorism has no legitimate connection to their religion?" Serwer asked. "I personally have no problem talking about Islamic extremism, but would it make the fight against it more successful if our officials were willing to call it that? I doubt it."

Serwer added that using the label could alienate moderate Muslims and hinder efforts to get Muslims on board in the fight against ISIS.

"Anything that stands in the way of Muslims joining the fight against ISIS is not a good thing," he said.

Bruce Riedel, a former CIA officer who now directs the Intelligence Project at the Brookings Institution, said the debate is just semantics.

"Whether or not we call it Islamic terrorism is not the issue," Riedel said in an interview Sunday, pointing to actions the administration takes rather than rhetoric.

But this seems to have become a debate that goes beyond the words "radical Islamic terrorism," right?

Republican criticism of Obama's refusal to use the term goes hand in hand with their critique of his strategy to fight ISIS in Iraq and Syria -- that Obama has not done enough to keep the country safe.

And it also goes toward a broader perception that Trump has fueled throughout his campaign to succeed Obama as commander-in-chief: that political correctness is holding the U.S. back.

Trump has repeatedly dismissed criticism of his numerous controversial policies --including banning on all foreign Muslims from entering the U.S. -- as the forces of political correctness at work.

And Obama's refusal to say the words "radical Islamic terrorism" present another opportunity for Trump to hammer his message.

"If we do not get tough and smart real fast, we are not going to have a country anymore," he warned Sunday. "I am trying to save lives and prevent the next terrorist attack. We can't afford to be politically correct anymore."

Has not using this terminology affected policy?

The Obama administration has engaged in a wide-ranging drone war against terrorists abroad since taking office and as the ISIS threat has grown has expanded U.S. forces taking on "advise and assist" roles with local troops in Syria and Iraq to root out ISIS. It has also kept more troops in Afghanistan than originally slated as the situation there has remained unstable.

It hasn't, however, taken as aggressive a stance as many Republicans have argued for in Iraq and in Syria, and it has taken out more U.S. forces from Iraq and Afghanistan than the GOP would have liked to see.

On the other hand, terrorism experts say lone wolf attacks by people radicalized online are almost impossible to detect and stop.

Still, Dubowitz said that he thinks that "the administration has wrongly downplayed the motivating and mobilizing ideology that underpins the threat."

To Reidel, however, "The issue is what do we do about it, and the President has done far more about Islamic terrorists like Osama bin Laden than the presumptive Republican candidate ever has."